Accession Number:

AD0420116

Title:

ON THE USE OF THE CALCULUS OF VARIATIONS IN TRAJECTORY OPTIMIZATION PROBLEMS,

Descriptive Note:

Corporate Author:

RAND CORP SANTA MONICA CALIF

Personal Author(s):

Report Date:

1963-10-01

Pagination or Media Count:

65.0

Abstract:

The theory of the calculus of variations is reviewed, including such subjects as the EulerLagrange equations, the transversality condition, the problems of Bolza, Lagrange, and Mayer, the corner condition, and the Weierstrass condition. Applications to a number of problems are given. These include that of a damped harmonic oscillator that is to be brought to rest in the shortest possible time. This problem is sufficiently simple to allow a clear demonstration of the theory. The close relationship between the ballistic perturbation theory and the calculus of variations is explained. The perturbation theory is then applied to the case of the trajectory in a constant gravity field. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE